Logarithmic curve with spiralling cross-section
Have you tried the tilt property of the curve's control points?

If you select one or more curve vertex and press Ctrl + T you enter tilt editing mode where you can control the twisting effect of the curve.

Depending on how your curve was built you can control this for one or more vertex at a time.

If you need to make a smooth gradient across a multitude of points you can use Proportional editing O key to affect adjacent vertex. Use Mouse wheel  to adjust the affected radius.